I should be able to equip you soon with a web browsing benchmark based on Firefox's Talos suite (https://wiki.mozilla.org/Buildbot/Talos). The most representative test (tp5) unfortunately depends on a data set that we can't distribute; but there are SunSpider and Dromaeo suites as well, and I am sure that we can arrange nightly tp5 runs within Mozilla. Let's work out what spectrum of hardware / kernel / userland options you'd like to cover with this benchmark.
Cheers, - Michael